Question 374855
The general equation for a quadratic is, {{{y=ax^2+bx+c}}}
{{{0=a(-1)^2+b(-1)+c}}}
1.{{{a-b+c=0}}}
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{{{12=a(2)^2+b(2)+c}}}
2.{{{4a+2b+c=12}}}
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{{{8=a(-2)^2+b(-2)+c}}}
3.{{{4a-2b+c=8}}}
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Subtract eq. 1 from eq. 2,
{{{4a+2b+c-a+b-c=12-0}}}
{{{3a+3b=12}}}
4.{{{a+b=4}}}
Subtract eq. 1 from eq. 3,
{{{4a-2b+c-a+b-c=8-0}}}
5.{{{3a-b=8}}}
Add eq. 4 and eq 5 together,
{{{a+b+3a-b=4+8}}}
{{{4a=12}}}
{{{a=3}}}
Then from eq. 4,
{{{3+b=4}}}
{{{b=1}}}
Then from eq. 1,
{{{3-1+c=0}}}
{{{c=-2}}}
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{{{highlight(f(x)=3x^2+x-2)}}}
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{{{drawing(300,300,-5,5,-5,20,grid(1),
circle(-1,0,0.2),
circle(2,12,0.2),
circle(-2,8,0.2),
graph(300,300,-5,5,-5,20,0,3x^2+x-2))}}}